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There are several problems in physics, such as kinetic energy equation, wave equation, anomalous diffusion process, and viscoelasticity that are described well in the fractional differential equation form. Therefore, the solutions with elementary solution method cannot be solved and described deliberately with detailed physics of the problems, so these problems are solved with the help of special operators such as Mittag–Leffler (M–L) functions equipped with Riemann–Liouville (R–L) fractional operators. Hence, keeping in view the above-mentioned problems in physics in the current study, the generalized properties are derived M–L functions connected with R–L fractional operators that are investigated in the generalized form. These extended special operators will be used for the solutions of generalized kinetic energy equation. The M–L function is a fundamental special function with a wide range of applications in mathematics, physics, engineering, and various scientific disciplines. Ayub et al. gave the definition of newly extended M–L (p,s,k)\left(p,s,k) function. Also, they gave its convergence condition and found several results relevant to that. The purpose of this study is to investigate newly extended M–L function and study its elementary properties and integral transforms such as Whittaker transform and fractional Fourier transform. The R–L fractional operator is a fundamental concept in fractional calculus, a branch of mathematics that generalizes differentiation and integration to non-integer orders. In this study, we discuss the relation of M–L (p,s,k)\left(p,s,k)-function and R–L fractional operators. In some cases, fractional calculus is used to describe kinetic energy equations, particularly in systems where fractional derivatives are more appropriate than classical integer-order derivatives. The M–L function can appear as a solution or as a part of the solution to these fractional kinetic energy equations. Also, we gave the generalization of kinetic energy equation and its solution in terms of newly extended M–L function.

BackgroundNonalcoholic fatty liver disease (NAFLD) is common among patients with type 2 diabetes mellitus (T2DM) and is associated with increased risk for coronary atherosclerosis and acute cardiovascular (CV) events. We employed the validated, non-invasive Angulo NAFLD fibrosis score (FS) in an intervention study in patients with T2DM and recent acute coronary syndrome (ACS) to determine the association of FS with CV risk and treatment response to apabetalone. Apabetalone is a novel selective inhibitor of the second bromodomain of bromodomain and extra-terminal (BET) proteins, epigenetic regulators of gene expression.MethodsThe Phase 3 BETonMACE trial compared apabetalone with placebo in 2,425 patients with T2DM and recent ACS. In this post hoc analysis, we evaluated the impact of apabetalone therapy on CV risk, defined as a composite of major adverse cardiovascular events (MACE: CV death, non-fatal myocardial infarction [MI], or stroke) and hospitalization for heart failure (HHF) in two patient categories of FS that reflect the likelihood of underlying NAFLD. Patients were initially classified into three mutually exclusive categories according to a baseline Angulo FS 0.675 (F3-F4), where F0 through F4 connote fibrosis severity none, mild, moderate, severe, and cirrhosis, respectively. The composite of ischemic MACE and HHF in the placebo group was higher in indeterminant and F3-F4 categories compared to the F0-F2 category (17.2% vs 15.0% vs 9.7%). Therefore, for the present analysis, the former two categories were combined into an elevated NAFLD CVD risk group (FS+) that was compared with the F0-F2 group (lower NAFLD risk, FS0-2).ResultsIn 73.7% of patients, FS was elevated and consistent with a moderate-to-high likelihood of advanced liver fibrosis (FS+); 26.3% of patients had a lower FS (FS0-2). In the placebo group, FS+ patients had a higher incidence of ischemic MACE and HHF (15.4%) than FS0-2 patients (9.7%). In FS+ patients, addition of apabetalone to standard of care treatment lowered the rate of ischemic MACE compared with placebo (HR = 0.79; 95% CI 0.60-1.05; p=0.10), HHF (HR = 0.53; 95% CI 0.33-0.86; p=0.01), and the composite of ischemic MACE and HHF (HR = 0.76; 95% CI 0.59-0.98; p=0.03). In contrast, there was no apparent benefit of apabetalone in FS0-2 patients (HR 1.24; 95% CI 0.75-2.07; p=0.40; HR 1.12; 95% CI 0.30-4.14; p=0.87; and HR 1.13; 95% CI 0.69-1.86; p=0.62, respectively). Over a median duration of 26.5 months, FS increased from baseline in both treatment groups, but the increase was smaller in patients assigned to apabetalone than to placebo (p=0.04).ConclusionsAmongst patients with T2DM, recent ACS, and a moderate-to-high likelihood of advanced liver fibrosis, apabetalone was associated with a significantly lower rate of ischemic MACE and HHF and attenuated the increase in hepatic FS over time.

BackgroundEpigenetic changes may contribute importantly to cognitive decline in late life including Alzheimer's disease (AD) and vascular dementia (VaD). Bromodomain and extra-terminal (BET) proteins are epigenetic "readers" that may distort normal gene expression and contribute to chronic disorders.ObjectiveTo assess the effects of apabetalone, a small molecule BET protein inhibitor, on cognitive performance of patients 70 years or older participating in a randomized trial of patients at high risk for major cardiovascular events (MACE).MethodsThe Montreal Cognitive Assessment (MoCA) was performed on all patients 70 years or older at the time of randomization. 464 participants were randomized to apabetalone or placebo in the cognition sub-study. In a prespecified analysis, participants were assigned to one of three groups: MoCA score≥26 (normal performance), MoCA score 25-22 (mild cognitive impairment), and MoCA score≤21 (dementia). Exposure to apabetalone was equivalent in the treatment groups in each MoCA-defined group.ResultsApabetalone was associated with an increased total MoCA score in participants with baseline MoCA score of≤21 (p = 0.02). There was no significant difference in change from baseline in the treatment groups with higher MoCA scores. In the cognition study, more patients randomized to apabetalone discontinued study drug for adverse effects (11.3% versus 7.9%).ConclusionIn this randomized controlled study, apabetalone was associated with improved cognition as measured by MoCA scores in those with baseline scores of 21 or less. BET protein inhibitors warrant further investigation for late life cognitive disorders.

The current study aimed to assess the neuroprotective effect of Zn and Fe oxide nanoparticles biofabricated by Taverniera glabra in alloxan-induced diabetic rats. The experimental animals (160–200 g) were divided into nine groups (n = 9). The blood glucose, body weight, glucose-6-phosphate dehydrogenase (G6PD), superoxide dismutase (SOD), catalase test (CAT), lipid peroxidation (TBARS), glutathione (GSH), and acetylcholinesterase (AChE) activities were determined. Oral administration of nanoparticles and T. glabra methanol extract (TGME; 10 and 15 mg/kg b.w) significantly decreased the glucose level, increased the body weight, controlled the quantitative level of G6PD, and significantly decreased the levels of ALT, ALP, cholesterol, and creatinine. Moreover, TGME and their Zn and Fe oxide nanoparticles significantly restored the antioxidant enzymes (SOD, CAT, GPx, and GSH) that decreased during induced diabetes. In the diabetic group, a significant increase in TBARS was noted and recovered in diabetic animals (p < 0.05) as compared to glibenclamide. The AChE activity was significantly recovered by nanoparticles and TGME both in the blood and brain of the diabetic group (p < 0.05). Taken together, it can be suggested that TGME and Zn and Fe oxide nanoparticles significantly improved memory and could be considered as an effective biogenic nanomaterial for diabetes, Alzheimer’s disease, and oxidative stress.